Best Known (92, 92+24, s)-Nets in Base 4
(92, 92+24, 1049)-Net over F4 — Constructive and digital
Digital (92, 116, 1049)-net over F4, using
- 41 times duplication [i] based on digital (91, 115, 1049)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 19, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (72, 96, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 24, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 24, 257)-net over F256, using
- digital (7, 19, 21)-net over F4, using
- (u, u+v)-construction [i] based on
(92, 92+24, 4170)-Net over F4 — Digital
Digital (92, 116, 4170)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4116, 4170, F4, 24) (dual of [4170, 4054, 25]-code), using
- 66 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 17 times 0, 1, 28 times 0) [i] based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- 66 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 17 times 0, 1, 28 times 0) [i] based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
(92, 92+24, 1164527)-Net in Base 4 — Upper bound on s
There is no (92, 116, 1164528)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6901 759622 570117 158526 140594 324750 345872 863780 744667 753780 257440 725403 > 4116 [i]